Questions tagged [qutrit]

For questions related to quantum trits i.e. three-level (dimensional) quantum mechanical systems. They are higher dimensional analogues of qubits (aka quantum bits), which are two-level (dimensional) quantum mechanical systems.

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Matrix representation of the qutrit gate analogous to Pauli-$X$ gate

What is the qutrit gate analogous to the $X$ gate for qubits, i.e. NOT gate? and what is the matrix representation of that gate? I have searched on the Internet but couldn't find anything related. ...
Root Groves's user avatar
2 votes
1 answer
207 views

Finding the eigenvalues of a qutrit state

I am interested in the state: $\frac{1}{\sqrt{2}} (\left|11\right> + \left|22\right>)$ If I find the density matrix of this, I find the $9 \times 9$ matrix $\rho$. If I want to find the reduced ...
am567's user avatar
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3 votes
1 answer
82 views

Cirq seems to output 0 instead of |2> with qutrits

I am experimenting a bit with qutrits on Cirq and came across a problem: my output is 0 when it should be |2>. I defined my qutrit as follows: ...
Q.Ask's user avatar
  • 195
3 votes
1 answer
267 views

Defining a discrete quantum walk on a 3D hypercube

I am trying to implement at a discrete-time quantum walk on a 3D hypercube using cirq. I have three qubits for the position register: the $|x\rangle$ qubit, $|y\rangle$ qubit and $|z\rangle$ qubit, ...
Q.Ask's user avatar
  • 195
2 votes
1 answer
82 views

Is there a method to implement qutrit using qubits?

I want to implement 3 level system on a qubit quantum computer. Currently I feel I can use 2 qubits and encode the states of a 3-level system as such |0>=|00>, |1>=|01>, |2>=|10> The ...
Chetan Waghela's user avatar
1 vote
2 answers
140 views

Is there another parameterization of a qutrit 3-level system, besides Gell-Mann?

Question: Is there a parameterization of a a general qutrit 3-level system similar to: $$\rho = \begin{bmatrix} p_1 & r_{12}e^{-i\phi_{12}} & r_{13}e^{-i\phi_{13}}\\ \cdot & p_2 & r_{...
G Frazao's user avatar
  • 155
0 votes
1 answer
98 views

Interpretation of Qudit measurement output in cirq

Here [+1] represents X gate for qutrit. How the Counter value is coming to 5? which is the measurement outcome(q0q1q2->102). Even for (q0q1q2->101) also counter value is 5. In total, for this 3 ...
SDubey's user avatar
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1 vote
0 answers
54 views

Is there a general parametric transformation matrix form in bloch-space corresponding to the unitary operations on qutrits?

I've been looking into the structure of the Bloch sphere for qudits, and I am wondering if there is a transformation matrix (or rotation matrix) formula corresponding to high-dimensional quantum ...
Waing's user avatar
  • 11
5 votes
2 answers
784 views

How to write the three-qubit GHZ state in the Pauli basis?

How can one write the GHZ state defined in Ket notation as $|\psi\rangle= \frac{1}{\sqrt{2}} \left(|000\rangle + |111\rangle\right)$, in terms of Pauli matrices $\sigma_{1},\sigma_{2},\sigma_{3}$?
User101's user avatar
  • 598
6 votes
2 answers
549 views

Can we rotate Bloch vectors for qudits like we do with qubits in the Bloch sphere?

I have been looking into the Bloch vectors for qudits and have been wondering if we can do rotations that are similar to the rotations in the qubit Bloch sphere. Like, once we create a Bloch vector ...
Parmeet Singh EP 066's user avatar
10 votes
1 answer
741 views

What is the set of generators for the qutrit Clifford group?

According to this article, any Clifford gate, acting on $n$ qubits, can be generated by Hadamard, CNOT, and S gates. What are the set of generators for qutrit Cliffords?
BlackHat18's user avatar
  • 1,293
4 votes
0 answers
119 views

Can a triplet be a qutrit?

Original question A triplet is a space that consist of three states that have the same total angular momentum (spin 1). If we restrict ourselves to a set of quantum gates that keep triplet states in ...
Mauricio's user avatar
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4 votes
1 answer
480 views

Qutrit analogues of controlled Z and cc-Z gates

I am trying to look for the qutrit analogues of a controlled-Z, and a cc-Z (Z gate with two controls) for qubits. There is a previous answer that gives a qutrit analogue of a CNOT gate, but does not ...
BlackHat18's user avatar
  • 1,293
5 votes
1 answer
533 views

Cliffordness of the qutrit Hadamard gate

Consider a simple generalization of the Hadamard gate to qutrits, defined as follows. \begin{equation} \begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0\\ \frac{1}{\sqrt{2}} &...
BlackHat18's user avatar
  • 1,293
3 votes
0 answers
57 views

Can someone elaborate how to use Qutrits to do teleportation? And the unitary operation Bob needs to do? [duplicate]

I can understand doing teleportation by using qubits, however, I am stuck there when it comes to qutrits and the operation Bob needs to perform. Suppose Alice and Bob are sharing the most entangled ...
NewtoQC's user avatar
  • 39
2 votes
2 answers
199 views

Is there a quantum processor with physically implemented Toffoli gate?

Recently, I came across the article Realization of efficient quantum gates with a superconducting qubit-qutrit circuit where its authors proposed a physical implementation of three qubits quantum ...
Martin Vesely's user avatar
3 votes
1 answer
246 views

Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
Mark Spinelli's user avatar
1 vote
1 answer
64 views

How do we restrict to a limited number of dimensions, say 3 for qutrits, while using OAM states of light?

When a azimuthal phase $\mathrm{e}^{il\phi}$ is applied to gaussian beams having plane wavefront, they develop a corkscrew sort of structure and therefore possess an orbital angular momentum in ...
Devjyoti Tripathy's user avatar
1 vote
1 answer
205 views

Color-Space as Effective and Intuitive Qutrit Physical Realization? [closed]

Has anyone used or considered color-space and color superposition for Qutrit work? A classical color-sphere has black and white at its poles, a grey scale as its axis, pure spectral colors as a color-...
wave's user avatar
  • 39
3 votes
1 answer
1k views

Defining standard qubit gates for qutrits

I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,y\rangle \to |x,y+x \bmod 2\rangle....
Marco Falso's user avatar
4 votes
0 answers
57 views

What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
Paul B. Slater's user avatar
3 votes
1 answer
115 views

Computing with qutrits

I'm doing some calculations with qutrits and I need a unitary matrix $U$ that does the following: $$U|00\rangle = |12 \rangle - | 21\rangle $$ $$U|11\rangle = |20 \rangle - | 02\rangle $$ $$U|22\...
Apo's user avatar
  • 545
6 votes
0 answers
193 views

Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention: In their paper[1] conjecturing that holographic ...
Sanchayan Dutta's user avatar
6 votes
1 answer
632 views

Problem about qutrit teleportation protocol

I'm working through Scott Aaronson's Quantum Information Science problem sets, and I'm having trouble with a specific problem in ps5 (PDF). Specifically the following problem: A “qutrit” has the form ...
Joe's user avatar
  • 257
11 votes
2 answers
1k views

What are useful resources about the geometric of qutrits and its relation with Gell-Mann matrices?

I need some useful sources about the geometry of qutrit. Specifically related to the Gell-Mann matrix representation.
Azadeh Zohrabi's user avatar
3 votes
2 answers
2k views

Difference between 3 qubits, 2 qutrits & 1 six level qunit

What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?
user820789's user avatar
  • 3,302
7 votes
2 answers
497 views

Confusion regarding projection operator

Suppose we have a qutrit with the state vector $|\psi\rangle = a_0|0\rangle + a_1|1\rangle + a_2|2\rangle$, and we want to project its state onto the subspace having the basis $\{|0\rangle,|2\rangle\}$...
alphauser's user avatar
7 votes
2 answers
555 views

Why is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?

If I have the $X$ gate acting on a qubit and the $\lambda_6$ gate acting on a qutrit, where $\lambda_6$ is a Gell-Mann matrix, the system is subjected to the Hamiltonian: $\lambda_6X= \begin{pmatrix}0 ...
user1271772's user avatar
  • 13.5k
8 votes
2 answers
624 views

Are qutrits more robust to decoherence?

A string of $n$ qutrits has a state-space spanned by the $3^n$ different states $\lvert x \rangle $ for strings $x \in \{0,1,2\}^n$ (or $x \in \{-1,0,+1\}^n$, equivalently), while $n $ qubits can ...
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